Cryptology ePrint Archive: Report 2009/589

Information-set decoding for linear codes over Fq

Christiane Peters

Abstract: A code-based cryptosystem is considered secure if the best known
attack against it is information-set decoding. Stern's algorithm and
its improvements are well optimized and the complexity is reasonably
well understood. However, these algorithms only handle codes over F2.

This paper presents a generalization of Stern's
information-set-decoding algorithm for decoding linear codes
over arbitrary finite fields Fq and analyzes the complexity.
This result makes it possible to compute the security
of recently proposed code-based systems over non-binary fields.

As an illustration, ranges of parameters for generalized
McEliece cryptosystems using classical Goppa codes over
F31 are suggested for which the new information-set-decoding algorithm needs 2^128 bit operations.